<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</font>, <font color="Maroon" title="c6">c1</font>, <font color="Maroon" title="c7">c2</font>, <font color="Maroon" title="c8">d1</font>, <font color="Maroon" title="c9">d2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c10">A</font> = <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c11">B</font> = <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c7">c2</font>,<font color="Maroon" title="c9">d2</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">D</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> ;<br/>
<a NAME="E4:29"/><i><font color="Green" title="E13">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c11">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c11">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c12">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c12">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c12">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">C</font> = <font color="Maroon" title="c10">A</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Maroon" title="c11">B</font> as   <a href="matrix_1.html#NM4" title="MATRIX_1:NM.4">Matrix</a> of <font color="Maroon" title="c1">K</font> ;<br/>
<a NAME="E6:29"/><i><font color="Green" title="E14">A2</font></i>: 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>proof </b></a><div class="add">

<i><font color="Green" title="E15">A3</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1</span>)</span> = 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c10">A</font>
<b>by </b><i><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>
;<br/>
<a NAME="E2:29_1"/><i><font color="Green" title="E16">A4</font></i>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E17">A5</font></i>: <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c2">a1</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E2:29_1"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c4">b1</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:29_1"/>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="matrix_3.html#E1:29_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="matrix_3.html#E3:29_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:29"/><i><font color="Green" title="E15">A6</font></i>: 
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><b>proof </b></a><div class="add">

<i><font color="Green" title="E16">A7</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2</span>)</span> = 
 <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c10">A</font>
<b>by </b><i><a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>
;<br/>
<a NAME="E2:29_2"/><i><font color="Green" title="E17">A8</font></i>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E18">A9</font></i>: <span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c6">c1</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c10">A</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E2:29_2"><i><font color="Green" title="E17">A8</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D8" title="MATRIX_1:def.8">MATRIX_1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c8">d1</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:29_2"/>
 <a href="matrix_1.html#K8" title="MATRIX_1:func.8">Line</a> <font color="Maroon" title="c10">A</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="matrix_3.html#E1:29_2"><i><font color="Green" title="E16">A7</font></i></a>, <a class="txt" href="matrix_3.html#E3:29_2"><i><font color="Green" title="E18">A9</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:29"/><i><font color="Green" title="E16">A10</font></i>: 
(  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c10">A</font> &amp;  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c11">B</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E9:29"/><i><font color="Green" title="E17">A11</font></i>: 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_3"><b>proof </b></a><div class="add">

<i><font color="Green" title="E18">A12</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1</span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font>
<b>by </b><i><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>
;<br/>
<a NAME="E2:29_3"/><i><font color="Green" title="E19">A13</font></i>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E20">A14</font></i>: <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E8:29"><i><font color="Green" title="E16">A10</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c3">a2</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E8:29"><i><font color="Green" title="E16">A10</font></i></a>, <a class="txt" href="matrix_3.html#E2:29_3"><i><font color="Green" title="E19">A13</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c7">c2</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:29_3"/>
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="matrix_3.html#E1:29_3"><i><font color="Green" title="E18">A12</font></i></a>, <a class="txt" href="matrix_3.html#E3:29_3"><i><font color="Green" title="E20">A14</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:29"/><i><font color="Green" title="E18">A15</font></i>: 
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">d2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_4"><b>proof </b></a><div class="add">

<i><font color="Green" title="E19">A16</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2</span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c11">B</font>
<b>by </b><i><a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
2
<b>by </b><i><a class="ref" href="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></i>
;<br/>
<a NAME="E2:29_4"/><i><font color="Green" title="E20">A17</font></i>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">1,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E21">A18</font></i>: <span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E8:29"><i><font color="Green" title="E16">A10</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c5">b2</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<span class="p1">(<span class="default"><a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 = 
<font color="Maroon" title="c11">B</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E8:29"><i><font color="Green" title="E16">A10</font></i></a>, <a class="txt" href="matrix_3.html#E2:29_4"><i><font color="Green" title="E20">A17</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="matrix_1.html#D9" title="MATRIX_1:def.9">MATRIX_1:def 9</a></i>
<br/>.= 
<font color="Maroon" title="c9">d2</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:29_4"/>
 <a href="matrix_1.html#K9" title="MATRIX_1:func.9">Col</a> <font color="Maroon" title="c11">B</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">d2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="matrix_3.html#E1:29_4"><i><font color="Green" title="E19">A16</font></i></a>, <a class="txt" href="matrix_3.html#E3:29_4"><i><font color="Green" title="E21">A18</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:29"/><i><font color="Green" title="E19">A19</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c13">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c13">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c14">C</font> = <font color="Maroon" title="c13">C</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of 2,<font color="Maroon" title="c1">K</font> <b>by </b><i><a class="ref" href="matrix_2.html#T7" title="MATRIX_2:th.7">MATRIX_2:7</a></i>;<br/>
<a NAME="E13:29"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c14">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c14">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E14:29"/><b>then </b><i><font color="Green" title="E20">A20</font></i>: 
 <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c14">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="matrix_3.html#E11:29"><i><font color="Green" title="E19">A19</font></i></a>, <a class="ref" href="matrix_1.html#D5" title="MATRIX_1:def.5">MATRIX_1:def 5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c15">i</font>, <font color="Maroon" title="c16">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:29_5"/><i><font color="Green" title="E21">A21</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c14">C</font>
 ;<br/><a NAME="E2:29_5"/><b>then </b><i><font color="Green" title="E22">A22</font></i>: 
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 )
 <b>by </b><i><a class="txt" href="matrix_3.html#E14:29"><i><font color="Green" title="E20">A20</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:29_5_1_1"/>
( ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) or ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) )
 </span><b>by </b><i><a class="txt" href="matrix_3.html#E2:29_5"><i><font color="Green" title="E22">A22</font></i></a>, <a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_5_1_1_1"><b>case </b></a><a NAME="E1:29_5_1_1_1"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1 = 
<span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E6:29"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="matrix_3.html#E9:29"><i><font color="Green" title="E17">A11</font></i></a>, <a class="txt" href="matrix_3.html#E1:29_5"><i><font color="Green" title="E21">A21</font></i></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">c2</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></i>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,1
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_5_1_1_2"><b>case </b></a><a NAME="E1:29_5_1_1_2"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2 = 
<span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">d2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E6:29"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="matrix_3.html#E10:29"><i><font color="Green" title="E18">A15</font></i></a>, <a class="txt" href="matrix_3.html#E1:29_5"><i><font color="Green" title="E21">A21</font></i></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">d2</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></i>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 1,2
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_5_1_1_3"><b>case </b></a><a NAME="E1:29_5_1_1_3"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1 = 
<span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">c2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E7:29"><i><font color="Green" title="E15">A6</font></i></a>, <a class="txt" href="matrix_3.html#E9:29"><i><font color="Green" title="E17">A11</font></i></a>, <a class="txt" href="matrix_3.html#E1:29_5"><i><font color="Green" title="E21">A21</font></i></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">c2</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></i>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,1
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="29_5_1_1_4"><b>case </b></a><a NAME="E1:29_5_1_1_4"/>
( <font color="Maroon" title="c15">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2 = 
<span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c9">d2</font></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="matrix_3.html#E4:29"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="matrix_3.html#E7:29"><i><font color="Green" title="E15">A6</font></i></a>, <a class="txt" href="matrix_3.html#E10:29"><i><font color="Green" title="E18">A15</font></i></a>, <a class="txt" href="matrix_3.html#E1:29_5"><i><font color="Green" title="E21">A21</font></i></a>, <a class="ref" href="matrix_3.html#D4" target="_self" title="MATRIX_3:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">d2</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T114" title="FVSUM_1:th.114">FVSUM_1:114</a></i>
<br/>.= 
<font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> 2,2
<b>by </b><i><a class="ref" href="matrix_2.html#T6" title="MATRIX_2:th.6">MATRIX_2:6</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:29_5"/>
<font color="Maroon" title="c14">C</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">D</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> <font color="Maroon" title="c15">i</font>,<font color="Maroon" title="c16">j</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E16:29"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">b1</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c8">d1</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">b2</font> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <font color="Maroon" title="c7">c2</font>,<font color="Maroon" title="c9">d2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">b1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span> <a href="matrix_2.html#K6" title="MATRIX_2:func.6">][</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c3">a2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c7">c2</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">c1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">d1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c9">d2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="matrix_1.html#T28" title="MATRIX_1:th.28">MATRIX_1:28</a></i>;<br/>


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